Considerable effort has recently been directed toward developing optical systems such as communication systems using optical waves. A challenge often encountered in the design of such systems is the efficient generation of optical waves with wavelengths which are particularly suitable for use in such systems. For example, while efficient laser generating of infrared waves is commonly available, the direct generation of certain more desirable waves having shorter wavelengths is often considerably more difficult.
One approach to providing waves with more desirable wavelengths has been wavelength conversion whereby articles containing an optical medium are used to at least partially convert optical waves incident to the medium to optical waves having a different wavelength. For example, a frequently used wavelength conversion process involves second harmonic generation where an incident optical wave is directed through a medium (e.g., a nonlinear crystal) in which optical waves having wavelengths corresponding to the second harmonic of the wavelength of the incident optical wave are generated by interaction between the medium and the optical waves.
Typically in optical articles for wavelength conversion, waves of suitable wavelength are generated over the length of the medium. It is well known in designing such articles that unless means are provided for inhibiting destructive interference between the waves generated at various points along the medium length, the efficiency of wavelength conversion schemes such as second harmonic generation can be severely limited. Accordingly, there is generally a need to employ some technique to control the effects of such destructive interference.
In somewhat more theoretical terms, wavelength conversion systems may be generally addressed in terms of a propagation constant k for each of the interacting optical waves in the conversion medium. For the purposes of this description, k for each optical wave may be defined as equal to 2.pi.n/.lambda., where n is the refractive index of the medium and .lambda. is the wavelength of the wave. In view of the inverse relationship between the propagation constant and the wavelength, and the fact that the refractive index can be different for optical waves of different frequencies, the propagation constant for each of the interacting optical waves in the conversion medium can clearly be different.
Generally, for wavelength conversion the sum of frequencies of the interacting incident waves is equal to the sum of the frequencies of the waves generated by the interaction. To minimize the destructive interference between waves generated in the medium, it has generally been considered desirable that the sum of the propagation constants of the interacting incident waves also closely approximate the sum of the propagation constants of the waves generated by the interaction. In other words, for the optical waves involved in the wavelength conversion, it has been considered desirable for efficient wavelength conversion that the difference between the total propagation constants for the incident waves in the medium and the total propagation constants for the waves generated in the medium (i.e., the .DELTA.k for the medium) be about zero. Adjusting a wavelength conversion system to a condition where .DELTA.k is about zero is known as phase matching.
An optical parameter of some interest in wavelength conversion systems for a particular medium is the coherence length, coh, which is generally defined as ##EQU1## For conditions where .DELTA.k is about zero, it is evident that the corresponding coh is relatively large.
For purposes of further illustration, in a normal phase matching process involving the nonlinear interaction of three beams in a crystal system where two beams of incident optical waves having respective frequencies .omega..sub.1 and .omega..sub.2 and respective wavelengths .lambda..sub.1 and .lambda..sub.2 are directed through a medium (e.g., a crystal or a composite material) having a refractive index n(.omega.) which varies as a function of the optical wave frequency, to generate optical waves having a frequency .omega..sub.3 and a wavelength .lambda..sub.3, a beam propagation constant k is defined for each wave beam as equal to 2.pi.n(.omega.)/.lambda., and a .DELTA.k for the crystal system is represented by the relationship: ##EQU2##
The maximum output intensity occurs in such a system when under conditions where the phase system is matched (i.e., .DELTA.k is zero). The intensity of output for a phase matched system generally increases in proportion to h.sup.2, the square of the crystal length, h.
For second harmonic generation systems the frequencies .omega..sub.1 and .omega..sub.2 are taken as equal and as one half of the frequency .omega..sub.3. Accordingly, the wavelengths .lambda..sub.1 and .lambda..sub.2 are twice the wavelength .lambda..sub.3 and .DELTA.k for second harmonic generation systems may be represented in terms of the above example, by the relationship: ##EQU3##
The coherence length for such second harmonic generation systems may thus be represented by the relationship: ##EQU4##
An alternate example of a wave conversion scheme involves generating two waves with wavelengths .lambda..sub.5 and .lambda..sub.6 from a single input wave of wavelengths .lambda..sub.4.
Several techniques have been demonstrated or proposed for achieving efficient phase matching. (See, for example, F. A. Hopf et al., Applied Classical Electrodynamics, Volume II, Nonlinear Optics, John Wiley & Sons, 1986, pp. 29-56.) The most common of these are the angle and temperature tuning techniques used in nearly all current applications such as second harmonic generation and sum and difference frequency generation. In angle tuning of bulk material such as a single crystal, the orientation of the crystal relative to the incident light is adjusted to achieve phase matching. The technique is generally considered inappropriate for use in articles such as waveguides which by nature of their design must be oriented in a particular direction with regard to incident waves. Temperature tuning relies on the temperature dependence of the birefringence of the material and may be used for waveguides as well as bulk material. However, for many materials the temperature dependence of the birefringence is large and, although temperature tuning is possible for waveguides in these materials, a high degree of temperature control must be provided (e.g., .+-.1.degree. C.). In optical materials where the temperature dependence of the birefringence is small (e.g., KTiOPO.sub.4), although a high degree of temperature control is necessary, the range of wavelengths over which temperature tuning is possible for waveguides is small.
Phase matching for second harmonic generation using periodic variations in the refractive index to correct for the fact that .DELTA.k is not equal to 0, can be accomplished by reflecting back both the fundamental and second harmonic beams in such a way that the reflected beams are phase matched (see, for example, S. Somekh, "Phase-Interchangeable Nonlinear Optical Interactions in Periodic Thin Films," Appl. Phys. Lett., 21, 140 (1972)). As with the methods above, the intensity of the second harmonic output increases with the square of the length of the material used. However, since only a small fraction of the beams are reflected, the overall efficiency of this method is even less than the methods discussed above.
Other "quasi" phase matching techniques have been demonstrated which involve periodic domain reversals or internal reflection (see J. A. Armstrong et al., "Interactions between Light Waves in a Nonlinear Dielectric", Phys. Rev., 127, 1918 (1962)). For example, Hopf et al., supra, discloses at page 52 segments of nonlinear optical material where the nonlinear optical coefficient is modulated at a period equal to the coherence length for the waves in the material.
Other modulated waveguide schemes have been described in the art which can give phase matching by using lengths of adjacent materials which are equal to the coherence length. However, these periodically modulated schemes can be very sensitive to waveguide parameters, such as waveguide depth and modulation period, and are not highly efficient with respect to conversion.
There remains a need for wavelength conversion schemes for efficiently converting fundamental optical waves to useful alternate wavelengths.